When he spoke in Columbia several years ago, Fr. Benedict Groeschel, CFR, said that, in his experience, the higher you go in any given “denomination,” you’re generally more likely to find people who are reasonable and open to dialogue. He told a story of giving an address to a Baptist seminary once on the Marian dogmas and how they reinforce authentic Christology. He said the ordained ministers and the theology professors all nodded in agreement. The students and other laity present got angrier and angrier as his talk progressed.
I’ve only ever met one SSPX family “IRL” that I can recall. It was at the Traditional Latin Mass the Priestly Fraternity of St. Peter (FSSP; the Order established by St. John Paul II for former SSPX members who were willing to return) used to offer monthly in Columbia–ironically, after Summorum Pontificum, they said they could no longer afford to drive from Atlanta every month unless the attendance increased. They offered to train one of the local priests. The only one who was willing was transferred, and no other pastor would volunteer to host or celebrate the Extraordinary Form.
Anyway, one of the only times I brought my whole family, there was this “nice” young family visiting their family for the holidays (I am not being politically correct; I forget which holiday it was). Our kids played with their kids while we talked after Mass.
They told us, “We only came here because there wasn’t an SSPX parish nearby. . . . ” They actually said they felt guilty for attending a “fake” Latin Mass and that, back home, they had both FSSP and SSPX but attended the latter. That, to me, summed up the problem and crushed any hope of formal reconciliation.
Bishop Fellay seems like a man of good will. He may get some of the other bishops and many of the priests to agree to reconciliation with Rome, but the priests and the laity already have the freedom to rejoin “full communion” (I’m choosing my words carefully) if they want. The priests can join the FSSP. The laity can just come to a local EF, but they won’t, because they fundamentally oppose the “New Church.” If Rome tomorrow said, “The suspension of SSPX is lifted, and they are in full communion and enjoy full canonical status as a [personal prelature or ordinariate],” there would still be Ross Perot’s “Giant Sucking Sound” of people defecting to Williamson’s group, the SSPV, etc.
Most people think the Mass is the issue, but it’s really a relatively small issue. The real problems the SSPX and other (for lack of a better term) “RadTrad” groups have stem from the documents: the vague wording, the teachings on religious liberty, _Nostra Aetate_ (which Pope Benedict XVI said was open to criticism for its naivete), etc. The fundamental issue of the “schism” (for lack of a better word), though not an official SSPX position, was the new rite of episcopal ordination. Bishop Fellay and other critics of the Second Vatican Council argued that the new rite has key points in which it diverts from the common traditions of all Catholic rites in history that render all post-Vatican II episcopal ordinations, in their view, invalid–including that of Josef Ratzinger. That is why Bishop Fellay ordained the group of four relatively young priests as bishops in 1988 against Vatican approval: to ensure in his view a valid line of Apostolic Succession, but ignoring that the ordinations would be canonically illicit and incurring excommunication on himself and the four young valid but illicit bishops.
When B16 succeeded St. John Paul II, the SSPX website got friendlier to Rome. It praised him and featured him prominently when he lifted the excommunications of the four bishops and opened discussion. It praised him even more when he issued Summorum Pontificum. Then suddenly it got very quiet. Rome made an offer. The SSPX refused. Controversial Bishop Richard Williamson was expelled but Fellay started sounding like Martin Luther.
The Benedict, for whom reconciliation with SSPX was a target of his papacy (how could the Church expect to heal centuries of other divisions without starting from the most recent?) gave his radio address saying it’s OK to criticize _Nostra Aetate_. He appointed Archbishop Gerhard Muller, often seen as something of a “liberal” to many of us because of his sympathy for liberation theology and his calls for St. JPII to retire, as Prefect of the Congregation for the Doctrine of Faith. Then, a few months later, after few headline-grabbing statements, Benedict resigned. His resignation of course created the situation of “two Popes,” a scenario which many traditionalists and many who were not previously “traditionalists” saw as potentially fulfilling warnings from various saints and visionaries.
There is so much pride and anger and hard-heartedness mixed up in all of this. I don’t doubt there are forces at work in the Vatican who squashed the talks and probably contributed to the Holy Father’s decision to resign, but there is so much hard-heartedness among the rank and file of the SSPX that, if Rome issued a statement tomorrow saying, “The faculties of all bishops and priests of the Society of St. Pius X are reinstated, and the Society will enjoy canonical status as an Ordinariate,” even then you’d hear Ross Perot’s “Giant Sucking Sound” of SSPX members starting yet another group, joining Williamson’s group, or joining the Society of St. Pius V.

St. Pius X and St. John Paul II, pray for unity of the Pilgrim Church on Earth.

The issue of invalidity occurs if there was a defect in either form, matter, intention or minister (which sometimes occurred in the new rite, especially because of experimentation – e.g., the Vatican repeatedly rejected the USCCB’s revised rite of priestly ordination, as it was deemed doubtful for validity).

Second, it was Archbishop Marcel Lefebvre and Bishop Antonio de Castro Mayer who did the 1988 Episcopal Consecrations; not Bishop Fellay (he was one of the four consecrated). Furthermore, this was not done because the new rite was invalid (and stated above), but to ensure the continuance of the traditional priesthood, to provide for the needs of the SSPX’s members, religious, and faithful dependent upon it, and to fulfill their duty as bishops of the Catholic Church. See this study for more details: http://sspx.org/en/news-events/news/now-studies-1988-consecrations-3187 as well as Archbishop Lefebvre’s sermon: http://sspx.org/en/news-events/news/echos-econe-25-years-ago-2004.

I think you might find it useful to get a better idea of what the SSPX really stands for and what it is actually like (as opposed to the rumors, hearsay and even poor examples). With this in mind, I would suggest seeing these video trailers about Archbishop Lefebvre and the SSPX:
-http://sspx.org/en/media/video/archbishop-lefebvre-documentary-1843
-http://sspx.org/en/media/video/forty-years-fidelity-dvd-excerpts-2756

Here’s the thing: I have read everything on the SSPX website, and every time I’ve ever tried to defend their positions, I’ve been informed by SSPX members that they hold the positions I described herein. Plus, if those *aren’t* the problems! what are they?